#"Let's do this step by step:"#
# \qquad \qquad f(x) = 10 sin ({πx}/6 - {2π}/3) +50 \qquad \quad => #
# f'(x) = [ 10 sin ({πx}/6 - {2π}/3) ]' + [ 50 ]' \qquad \qquad \qquad \qquad \quad "by Sum Rule" #
# = 10 [ sin ({πx}/6 - {2π}/3) ]' + 0 \qquad \qquad \qquad \qquad "by Rules for Constants" #
# = 10 cos ({πx}/6 - {2π}/3) cdot ({πx}/6 - {2π}/3)' \qquad "Chain Rule with sin" #
# = 10 cos ({πx}/6 - {2π}/3) cdot ({π}/6 x- {2π}/3)' \qquad \qquad \qquad \quad \ "rewrite a little" #
# = 10 cos ({πx}/6 - {2π}/3) cdot [ ({π}/6) - 0].\qquad \qquad \ "Rules for Constants" #
#"Note that there are no more differentiations asked for now in" #
# "the last expression."#
#"This means we are at the beginning of the Simplification "#
#"Phase. No more derivatives now."#
# = 10({π}/6) cos ({πx}/6 - {2π}/3) #
# = {5π}/3 cos ({πx}/6 - {2π}/3). #
#"This is our answer."#
#"Summarizing:"#
# \qquad \qquad f(x) = 10 sin ({πx}/6 - {2π}/3) +50 \qquad \quad => #
# \qquad \qquad \qquad \qquad \qquad \qquad f'(x) = {5π}/3 cos ({πx}/6 - {2π}/3).#
